Summary
The notion of uniform distribution of a sequence is generalized to sequences of partitions in a separable metric space X. Results concern Riemann integrability with respect to a probability λ on X, and Riemann approximations of Lebesgue integrals.
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References
N. G. De Brujin -K. A. Post,A remark on uniformly distributed sequences and Riemann integrability, Indag. Math.,30 (1968), pp. 149–150.
J.Dugundji,Topology, Allyn and Bacon Inc. (1966).
E. Hlawka,The Theory of Uniform Distribution, AB Academic Publishers, Berkhamsted (1984).
K.Jacobs,Measure and Integral, Academic Press (1978).
S.Kakutani,A problem of equidistribution on the unit interval, in:Measure Theory, Oberwolfach (1975), pp. 369–375; Lect. Notes in Math.,541, Springer-Verlag (1976).
L.Kuipers - H.Niederreiter,Uniform Distribution of Sequences, J. Wiley (1974).
K. Schmidt,Über einen Zusammenhang zwischen gleichverteilten Punkt- and Massfolgen, J. Reine Angew. Math.,244 (1970), pp. 94–96.
L.Schwartz,Radon Measure on Arbitrary Topological Spaces and Cylindrical Measures, Tata Institute of Fundamental Research, Oxford Univ. Press (1973).
P. Morales,Mean value theorem for the m-integral of Dinculeanu, Canad. Math. Bull.,15 (2) (1972), pp. 243–251.
H. Niederreiter,On the existence of uniformly distributed sequences in compact spaces, Compositio Math.,25 (1972), pp. 93–99.
L. R.Parthasarathy,Probability Measures on Metric Spaces, Academic Press (1967).
H. Weyl,Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann.,77 (1916, reprint 1964), pp. 313–352.
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Lavoro presentato al terzo Convegno nazionale «Analisi reale e teoria della misura» (Capri, 12–16 settembre 1988).
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Chersi, F., Volčič, A. λ-Equidistributed sequences of partitions and a theorem of the De Bruijn-Post type. Annali di Matematica pura ed applicata 162, 23–32 (1992). https://doi.org/10.1007/BF01759997
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DOI: https://doi.org/10.1007/BF01759997